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I don't know if it's visa free or visa on arrival or just easy visa... I just know that in theory (and in pre-covid times) you could go to Georgia and you are even allowed to work there if you are working for clients outside of the country (remote work).
Happy to see you look for option. I believe that if you look you may actually find some unconventional options which can make your life better on a Lebanese passport.
There are some other countries that offer residence if you prove that you receive a regular income from abroad.
Due to Covid many countries may refuse entry at the moment.